Predicting Depth and Path of Subsurface Crack Propagation at Gear Tooth Flank under Cyclic Contact Loading

Document Type: Research Paper

Authors

Mechanical Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

Abstract

In this paper, a two-dimensional computational model is proposed for predicting the initiation position and propagation path of subsurface crack of spur gear tooth flank. In order to simulate the contact of teeth, an equivalent model of two contacting cylinders is used. The problem is assumed to be under linear elastic fracture mechanic conditions and finite element method is used for numerical study. An initial subsurface crack is considered in the model at different depths. For each position of the initial crack, moving contact loading is applied to the part and value of ∆KII is obtained for the crack tips. The position of maximum ∆KII is selected as the location of crack initiation. It is shown that the subsurface crack appears at the maximum shear stress point. The maximum tangential stress criterion is used to determine the crack growth angle. The crack is incrementally propagated until the crack tip reaches the part surface and a cavity is formed on the tooth surface. Analyzing the stress field and stress intensity factors are performed in ABAQUS software. The obtained results for the depth and shape of the spall are in good agreement with the experimental results reported in literature.

Keywords

[1] Boresi A.P., Schmidt R.J., Sidebottom O.M., 1993, Advanced Mechanics of Materials, John wiley & sons, Hoboken.
[2] Spitas V., Spitas C., 2007, Numerical and experimental comparative study of strength-optimised AGMA and FZG spurgears, Acta Mechanica 193: 113-126.
[3] Spitas C., Spitas V., Amani A., Rajabalinejad M., 2014, Parametric investigation of the combined effect of whole depth and cutter tip radius on the bending strength of 20◦ involute gear teeth, Acta Mechanica 225: 361-371.
[4] Ding Y., Rieger N.F., 2003, Spalling formation mechanism for gears, Wear 254: 1307-1317.
[5] Way S., 1935, Pitting due to rolling contact, Journal of Applied Mechanics, Transactions of ASME 57: A49-A58.
[6] Sraml M., Flasker J., Potrc I., 2003, Numerical procedure for predicting the rolling contact fatigue crack initiation, International Journal of Fatigue 25: 585-595.
[7] Sraml M., Flasker J., 2007, Computational approach to contact fatigue damage initiation analysis of gear teeth flanks, International Journal of Advanced Manufacturing Technology 31: 1066-1075.
[8] Alfredsson B., Dahlberg J., Olsson M., 2008, The role of a single surface asperity in rolling contact fatigue, Wear 264: 757-762.
[9] Ding Y., Gear J.A., 2009, Spalling depth prediction model, Wear 267: 1181-1190.
[10] Beheshti A., Khonsari M.M., 2011, On the prediction of fatigue crack initiation in rolling/sliding contacts with provision for loading sequence effect, Tribology International 44: 1620-1628.
[11] Moorthy V., Shaw B.A.,2013, An observation on the initiation of micro-pitting damage in as-ground and coated gears during contact fatigue, Wear 297: 878-884.
[12] Glodez S., Winter H., Stuwe H.P., 1997, A fracture mechanics model for the wear of gear flanks by pitting, Wear 208: 177-183.
[13] Glodez S., Ren Z., 1998, Modelling of crack growth under cyclic contact loading, Theoretical and Applied Fracture Mechanics 30: 159-173.
[14] Flasker J., Fajdiga G., Glodez S., Hellen T.K., 2001, Numerical simulation of surface pitting due to contact loading, International Journal of Fatigue 23: 599-605.
[15] Ren Z., Glodez S., Fajdiga G., Ulbin M., 2002, Surface initiated crack growth simulation in moving lubricated contact, Theoretical and Applied Fracture Mechanics 38: 141-149.
[16] Aslantas K., Tasgetiren S., 2004, A study of spur gear pitting formation and life prediction, Wear 257: 1167-1175.
[17] Glodez S., Abersek B., Flasker J., Ren Z., 2004, Evaluation of the service life of gears in regard to surface pitting, Engineering Fracture Mechanics 71: 429-438.
[18] Fajdiga G., Flasker J., Glodez S., 2004, The influence of different parameters on surface pitting of contacting mechanical elements, Engineering Fracture Mechanics 71: 747-758.
[19] Jurenka J., Spaniel M., 2014, Advanced FE model for simulation of pitting crack growth, Advances in Engineering Software 72: 218-225.
[20] Glodez S., Ren Z., Flasker J., 1998, Simulation of surface pitting due to contact loading, International Journal for Numerical Methods in Engineering 43: 33-50.
[21] Fajdiga G., Glodez Kramar, J., 2007, Pitting formation due to surface and subsurface initiated fatigue crack growth in contacting mechanical elements, Wear 262: 1217-1224.
[22] Fajdiga G., Sraml M., 2009, Fatigue crack initiation and propagation under cyclic contact loading, Engineering Fracture Mechanics 76: 1320-1335.
[23] Hannes D., Alfredsson B., 2013, Modelling of surface initiated rolling contact fatigue damage, Procedia Engineering 66: 766-774.
[24] Hannes D., Alfredsson B., 2012, Surface initiated rolling contact fatigue based on the asperity point load mechanism - A parameter study, Wear 294: 457-468.
[25] Davis J.R., 2005, Gear Materials, Properties, and Manufacture, ASM International, First Edition.
[26] Asi O., 2006, Fatigue failure of a helical gear in a gearbox, Engineering Failure Analysis 13: 1116-1125.
[27] Moorthy V., Shaw B.A., 2012, Contact fatigue performance of helical gears with surface coatings, Wear 276-277: 130-140.
[28] Budynas R.G., Nisbett J.K., 2011, Shigley's Mechanical Engineering Design, McGraw-Hill, New York.
[29] Abaqus/CAE User’s Manual, Version 6.12, 2012.
[30] Rebbechi B., Oswald F.B., Townsend D.P., 1996, Measurement of gear tooth dynamic friction, NASA Technical Report ARL-TR-1165.
[31] Bomidi J.A.R., Sadeghi F., 2014, Three-demensional finite element elastic-plastic model for subsurface initiated spalling in rolling contacts, Journal of Tribology 136: 011402-0114011.
[32] Juvinall R.C., Marshek K.M., 2012, Fundamentals of Machine Component Design, John wiley & sons, Hoboken.
[33] Johnson K.L., 1985, Contact Mechanics, Cambridge University Press, Cambridge.
[34] Richard H.A., Fulland M., Sander M., 2005, Theoretical crack path prediction, Fatigue & Fracture of Engineering Materials & Structures 28: 3-12.
[35] Erdogan F., Sih G.C., 1963, On the crack extension in plates under plane loading and transverse shear, Journal of Basic Engineering 85: 519-525.
[36] Hertzberg R.W., 1996, Deformation and Fracture Mechanics of Engineering Materials, John Wiley & Sons, New Jersey.
[37] Tanaka K., 1974, Fatigue crack propagation from a crack inclined to the cyclic tensile axis, Engineering Fracture Mechanics 6: 493-507.